PRP Records

Probable Primes Top 10000

(177649 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
60014*6^89958-770002Lelio R Paula09/2014
600210^70000+8048770001Milton L. Brown05/2006
600310^69999+13485770000Patrick De Geest02/2007
600810^70000-927370000Patrick De Geest08/2009
6004(79*10^69999-7)/970000Robert Price01/2015
6007((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6005(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6006(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
600910^69999-8825169999Patrick De Geest08/2009
60102^232507+108969992Lelio R Paula04/2012
6011(17*2^232445+1)/569974Lelio R Paula08/2012
60127^82778+4869956Lelio R Paula09/2013
60137*2^232381+369955Lelio R Paula04/2014
60142^232362-11054169948Enzo Doria05/2014
60152^232326-11239169938Enzo Doria06/2014
60163^146575+23669935Lelio R Paula09/2013
601730^47341-2969929Norbert Schneider02/2014
60185^100040-6869925Lelio R Paula09/2013
60192^232045-1729569853Lelio R Paula04/2012
6020(2^231987+78557)/9569834Lelio R Paula05/2012
60212^231955+7424369826Yves Minet03/2011
60222^231946-1587369823Enzo Doria04/2013
602318^55618+9569816Lelio R Paula09/2013
60246^89712+5^(89712-1)69810Robert Price02/2016
60252^231870+13569800Lelio R Paula02/2012
6026(23*2^231827-1)/417969785Lelio R Paula01/2014
60272^231778+5461569773Lelio R Paula04/2012
6028(19*2^231780+1)/23569772Lelio R Paula08/2012
602914^60866+2769761Lelio R Paula09/2013
603013^62619-4469755Lelio R Paula09/2013
6031(2^231715-509203)/3569752Lelio R Paula05/2012
60322^231711-11046769752Enzo Doria05/2014
6033(19^54547+18^54547)/3769751Robert Price08/2013
6034(23*2^231697-1)/4569748Lelio R Paula01/2014
60352^231696-186149969748Enzo Doria03/2016
60362^231684-14769744Lelio R Paula02/2012
6037(23*2^231686-1)/118369743Lelio R Paula01/2014
60382^231591-47739769716Paul Bourdelais03/2013
603911^66916-42069686Enzo Doria08/2012
60405^99680-1370669674Enzo Doria02/2013
6041(8*10^69674-53)/969674Robert Price11/2014
6042(77*10^69656-23)/969657Robert Price10/2015
60436^89509+13169652Lelio R Paula09/2013
6044(78557*2^231349+1)/3569647Lelio R Paula06/2014
6045(11*10^69645+19)/369646Robert Price03/2016
604611^66875-2869644Lelio R Paula09/2013
60472^231347+7148369643Enzo Doria04/2016
6048(14^60763+3^60763)/1769641Robert Price04/2013
6049(4*10^69626+173)/369627Robert Price01/2017
60502^231289+25569625Lelio R Paula04/2012
60512^231234-11291369609Enzo Doria06/2014
6052(265*10^69602-7)/369604Robert Price07/2016
60532^231182-11284169593Enzo Doria06/2014
6054(15*2^231129+1)/2369577Lelio R Paula08/2012
60553^145806-2869568Lelio R Paula09/2013
6056(265*10^69554-7)/369556Robert Price07/2016
60572^231052-11315969554Enzo Doria07/2014
605811^66784-869549Lelio R Paula09/2013
6059Phi(104409,10)/229699969546Maksym Voznyy07/2015
60602^231016-11052369543Enzo Doria05/2014
60612^231014+57729457569543Lelio R Paula02/2016
606214^60658+6769522Lelio R Paula09/2013
60635^99418+3669491Lelio R Paula06/2013
60647^82203-3069470Lelio R Paula09/2013
60655^99359-2^9936069449Mike Oakes12/2010
6066(29*2^230684+1)/139569442Lelio R Paula08/2012
6067(19*10^69424+77)/369425Robert Price08/2016
606819^54287-9669420Lelio R Paula09/2013
60692^230541+5890569400Lelio R Paula04/2012
60702^230506+1270569390Lelio R Paula02/2013
60718*6^89156-569378Lelio R Paula09/2014
60722^230438-11134769369Enzo Doria05/2014
60732^230428-9969366Lelio R Paula02/2012
60743*10^69354+1769355Robert Price03/2017
6075(493*10^69340-7)/969342Robert Price07/2016
6076(41*10^69321+373)/969322Robert Price04/2017
60776^89072+5369312Lelio R Paula09/2013
6078155^31639+269300Lelio R Paula05/2013
60793*7^81965-469269Lelio R Paula09/2014
6080(86*10^69260-77)/969261Robert Price05/2016
60819*5^99087+469260Lelio R Paula09/2014
60823^145145+266069252Lelio R Paula09/2013
608311^66492-114069245Enzo Doria11/2012
60845*3^145129-469245Lelio R Paula04/2014
60857*3^145126+869244Lelio R Paula04/2014
608611^66480-237069232Enzo Doria12/2012
60872^229962-6569226Lelio R Paula02/2012
60882^229958-11073369225Enzo Doria05/2014
6089V(332407)69225Serge Batalov03/2015
60906^88959+769224Lelio R Paula09/2013
609115^58855-9469219Lelio R Paula09/2013
6092(2^229838+47)/1208169185Lelio R Paula04/2012
60933^144952+9869160Lelio R Paula09/2013
60945^98941-7269157Lelio R Paula06/2013
6095(17*2^229604-1)/22969117Lelio R Paula01/2014
60962^229585-106369112Yves Minet11/2012
6097(13*2^229567-1)/1969107Lelio R Paula01/2014
6098(13*2^229393-1)/569055Lelio R Paula01/2014
6099(53*10^69050-17)/969051Robert Price09/2015
61002^229305-186853369028Enzo Doria04/2016
61012^229297+138569026Lelio R Paula04/2012
610218^54986-244169023Enzo Doria03/2013
6103(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
61045^98736-1463669014Enzo Doria02/2013
6105(13^61949-5^61949)/869007Robert Price03/2013
6106(2^229227+5)/61169002Lelio R Paula04/2012
61072^229216-11327969001Enzo Doria07/2014
610810^68994+5191368995Patrick De Geest03/2016
611010^68994-10^5814-168994Serge Batalov01/2011
610910^68994-8294768994Patrick De Geest03/2016
6111(17*2^229136-1)/238168975Lelio R Paula01/2014
61122^229113+10768970Lelio R Paula02/2012
611311^66202-441068943Enzo Doria01/2013
611412^63883+568942Lelio R Paula07/2013
6115(9913*2^229002-1)/39990368935Lelio R Paula04/2015
61162^228962-11158168925Enzo Doria05/2014
61172^228944+8168920Henri Lifchitz01/2007
611811^66174-5468914Lelio R Paula09/2013
61192^228913-11126568910Enzo Doria05/2014
61202^228902+7351968907Enzo Doria04/2016
6121(47*2^228884+1)/6368901Lelio R Paula04/2015
61222^228821+7642768882Enzo Doria05/2016
61233^144340+5068868Lelio R Paula09/2013
61242^228758-11296768864Enzo Doria06/2014
61252^228743-11137968859Enzo Doria05/2014
61262^228741-11091168858Enzo Doria05/2014
6128lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
61273*5^98511-868857Lelio R Paula09/2014
61292^228717+46768851Lelio R Paula02/2011
6130Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6131(509203*2^228665-1)/3568840Lelio R Paula04/2015
61328^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
613311^66074-105068809Enzo Doria11/2012
61342^228484+18168781Lelio R Paula02/2012
61352^228479-5869568780Lelio R Paula04/2012
61362^228465-1585368775Enzo Doria04/2013
613711^66040-540068774Enzo Doria01/2013
6138(13*2^228441-1)/57568766Lelio R Paula01/2014
6139(17*2^228393+1)/29568752Lelio R Paula08/2012
61402*10^68744+4168745Robert Price01/2017
614111^66011-15068744Enzo Doria08/2012
6142(13*2^228304-1)/8168726Lelio R Paula01/2014
61432^228295-11107968724Enzo Doria05/2014
6144(3^144039+7)/2268723Lelio R Paula04/2012
6145(8*10^68722+49)/368723Robert Price03/2016
6146(35*10^68718+1)/968719Serge Batalov11/2010
61472^228271-22827168717Henri Lifchitz11/2004
61482^228257+8287568713Lelio R Paula02/2013
61493^144013+4068712Lelio R Paula09/2013
615013^61671-8668699Lelio R Paula09/2013
615117^55828-7268694Lelio R Paula09/2013
61526^88259+6168679Lelio R Paula09/2013
615318^54699-568663Lelio R Paula09/2013
615433^45216+268662Lelio R Paula05/2013
6156(2^228073-5)/368657Lelio R Paula04/2012
6155(2^(6*38012+1)-5)/368657Kevin Acres11/2013
61572^228055-11160768652Enzo Doria05/2014
61582^228054-11476168652Enzo Doria05/2015
61592^228041+118568648Lelio R Paula04/2012
61602^228040-103768647Yves Minet11/2012
61612*F(328450)-168642Henri Lifchitz12/2009
61625^98201-3468640Lelio R Paula06/2013
61639^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
61647*2^227780-368570Lelio R Paula04/2014
61652^227733-12168555Lelio R Paula02/2012
61662^227702-1696768546Enzo Doria05/2013
61672^227689-11165568542Enzo Doria05/2014
6168gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
61695^98051+268535Ray Chandler07/2011
61705*10^68524+5168525Robert Price01/2017
6171(11*10^68520-149)/368521Robert Price01/2017
617219^53573-7868507Lelio R Paula09/2013
6173(68*10^68504+13)/968505Ray Chandler10/2010
61749*5^98003+468503Lelio R Paula09/2014
61752^227528+5168493Lelio R Paula02/2012
61763^143497+868466Lelio R Paula04/2012
61772^227430-9568464Lelio R Paula02/2012
61783*5^97934-268454Lelio R Paula09/2014
617920^52613+7768452Lelio R Paula09/2013
61802^227371+3276968446Lelio R Paula04/2012
6181(3^143465+4)/2127042006768440Lelio R Paula04/2012
6182CopelandErdos(68433)68433Eric W. Weisstein08/2013
61832^227323+7543168432Enzo Doria04/2016
61842^227314-196568429Lelio R Paula04/2012
61852^227303-11061768426Enzo Doria05/2014
61877^80963+6668422Lelio R Paula07/2013
61862^227290+7384968422Enzo Doria04/2016
6188(14^59693-1)/1368415Paul Bourdelais06/2008
61892^227256-278624968411Enzo Doria03/2016
61908*10^68400-768401Dmitry Domanov11/2010
6191(15*2^227228-1)/58368401Lelio R Paula01/2014
61922^227210+186916968398Enzo Doria05/2016
61932^227159-183863568382Enzo Doria05/2015
61942^227115-780768369Lelio R Paula10/2009
61952^227078-4735568358Lelio R Paula04/2012
6196(2^227063-1017)/34968351Lelio R Paula04/2012
61972^227057+14809168351Lelio R Paula04/2012
61982^227046+18768348Lelio R Paula02/2012
619911^65608-72068324Enzo Doria11/2012
620033408!2-2^33408-168315Joe McLean05/2017
62012^226894-12368302Lelio R Paula02/2012
620210^68297+14155968298Patrick De Geest05/2013
620310^68297-9368297Robert Price05/2011
6204680^24107-679^2410768284Jean-Louis Charton07/2010
620512^63267+5968277Lelio R Paula07/2013
62062^226785-115968270Yves Minet11/2012
62077^80769+9068258Lelio R Paula07/2013
62082^226741+6658768256Yves Minet10/2010
62092^226720-11240368250Enzo Doria06/2014
6210(78557*2^226694+1)/368247Lelio R Paula06/2014
6211(83*10^68231+7)/968232Robert Price10/2015
621265^37636+1668231Lelio R Paula01/2016
62135^97615-4^(97615+1)68230Robert Price04/2016
621412^63200-4368205Lelio R Paula07/2013
6215-330*Bern(21940)/22379062073368201Serge Batalov04/2015
62163^142925+868068193Lelio R Paula06/2013
62173*2^226512-768188Lelio R Paula04/2014
621814^59484+5768177Lelio R Paula08/2013
621911^65438-219068147Enzo Doria12/2012
622091^34784-268144Lelio R Paula09/2013
6221(2^226336-3)*6-768135Gilbert Mozzo06/2016
6222(22*10^68133-37)/368134Robert Price05/2017
62235^97476+3668133Lelio R Paula06/2013
62243*5^97474-268132Lelio R Paula09/2014
622512^63130+4968129Lelio R Paula07/2013
62262^226281+538568118Lelio R Paula04/2012
62272^226257-304968111Yves Minet10/2014
6228(28*10^68107-43)/368108Robert Price04/2016
62292^226243-258768106Yves Minet07/2014
623020^52346-1168104Lelio R Paula09/2013
62312^226205-9968095Lelio R Paula02/2012
62322^226187-4968090Lelio R Paula02/2012
62333^142708+7668090Lelio R Paula06/2013
62347*10^68088-8968089Robert Price01/2017
62352^226154+7183968080Enzo Doria04/2016
6236(10^68078+59)/368078Serge Batalov12/2014
623814^59387+6968066Lelio R Paula08/2013
62372^226108-11342968066Enzo Doria07/2014
6239(24^49307-1)/2368053Robert Price04/2012
624015^57859-2868048Lelio R Paula08/2013
6241(509203*2^226003-1)/1368039Lelio R Paula04/2015
62422^226015-11136168038Enzo Doria05/2014
6243156*(10^(4*17000)-1)/101-168001Robert Price05/2014
62442^225878-101767997Lelio R Paula04/2012
62453*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
62463*2^225865+567993Lelio R Paula04/2014
624811^65284-582067987Enzo Doria01/2013
624719^53166+7067987Lelio R Paula08/2013
62492^225837+7540767984Enzo Doria04/2016
62503^142464-11265467973Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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